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CONFERENCE

Model Theory, Difference/Differential Equations and Applications
April 7 - 10, 2015

In the last decades, differential algebraic geometry, differential Galois theory and algebraic dynamics have benefitted from the close interaction with Model Theory, especially the model theory of fields with operators. Geometric model theory, both in the stable context and neostable counterparts, such as simplicity or o-minimality, provides an analysis of the underlying geometry of definable sets. Such an analysis is particularly powerful in combination with the Trichotomy Principle, known to hold both in differentially closed fields and in existentially closed difference fields.

Various model-theoretic tools, in particular sharpenings of the Trichotomy Principle, have been used in recent years with great success in algebraic dynamics, e.g. in connection with descent issues and the study of invariant subvarieties. Similar connections exist in the study of classical differential and difference equations, such as Painlevé equations (and its q-variants) and the differential equations satisfied by relevant analytic functions: the exponential function or the j-invariant, among others. These development relate to questions in diophantine geometry and transcendence theory.

The aim of the meeting is to present some of the major recent developments in these areas. Furthermore, we seek to bring together model-theorists and researchers in other fields of mathematics, from differential algebraic geometry to algebraic dynamics, as well as difference/differential Galois theory and arithmetic geometry.

Scientific Committee

Antoine Chambert-Loir (Université Paris-Sud)
Lucia Di Vizio (Université de Versailles St-Quentin-en-Yvelines)
Martin Hils (Université Paris Diderot)
Amador Martin-Pizarro (Université Lyon 1)
Thomas Scanlon (University of California, Berkeley)

Organizing Committee

Özlem Beyarslan (University of Bogazici, Turkey)
Martin Hils (Université Paris Diderot)
Amador Martin-Pizarro (Université Claude Bernard Lyon 1)

Speakers

• Daniel Bertrand (UPMC Paris 6)
  

Galois Groups of Logarithmic Equations : the Abelian Case

• Elisabeth Bouscaren (CNRS & Université Paris-Sud)

From Manin Mumford to Mordell-Lang via Model Theory

• Artem Chernikov (Université Paris Diderot)
  

Graph Regularity and Incidence Phenomena in Distal Structures

• James Freitag (UC Berkeley)

On Differential Chow Varieties

• Holly Krieger (MIT)

A Case of the Dynamical André-Oort Conjecture

• François Loeser (UPMC Paris 6)
  

Trace Formulas in Non-Archimedean Geometry

• Angus Macintyre (Queen Mary University of London)

On Quotients of Models of Peano Arithmetic by Principal Ideals

• Alice Medvedev (CUNY, New York)

Groups of Finite Rank in ACFA

• Samaria Montenegro-Guzman (Université Paris Diderot)
  

Model Theory of Pseudo Real Closed Fields

• Rahim Moosa (University of Waterloo, Canada)

Nonstandard Compact Complex Manifolds with a Generic Auto-Morphism

• Joel Nagloo (CUNY, New York)

On the Non-Generic Second Painlevé Equation

• Seiji Nishioka (Yamagata University) 

Double-Angle Formulae and Algebraic Independence

• Anand Pillay (University of Notre Dame)

Galois Groups of Logarithmic Equations : the Semi-Abelian Case

• Françoise Point (FNRS & Université de Mons)

Transfer Results in Topological Differential Fields

• Hiroshi Umemura (Nagoya University)

Quantum Picard-Vessiot Theory

• Lou Van den Dries (University of Illinois at Urbana-Champaign)

Newtonianity of Transseries

• Michael Wibmer (RWTH Aachen) 

Etale Difference Algebraic Groups